Computation of the Selmer groups of certain parametrized elliptic curves

S. Schmitt

Acta Arithmetica (1997)

  • Volume: 78, Issue: 3, page 241-254
  • ISSN: 0065-1036

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S. Schmitt. "Computation of the Selmer groups of certain parametrized elliptic curves." Acta Arithmetica 78.3 (1997): 241-254. <http://eudml.org/doc/206945>.

@article{S1997,
author = {S. Schmitt},
journal = {Acta Arithmetica},
keywords = {torsion groups; elliptic curves; sign of the functional equation; algorithm for computing the Selmer groups; 2-isogenies; generators of the Mordell-Weil groups},
language = {eng},
number = {3},
pages = {241-254},
title = {Computation of the Selmer groups of certain parametrized elliptic curves},
url = {http://eudml.org/doc/206945},
volume = {78},
year = {1997},
}

TY - JOUR
AU - S. Schmitt
TI - Computation of the Selmer groups of certain parametrized elliptic curves
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 3
SP - 241
EP - 254
LA - eng
KW - torsion groups; elliptic curves; sign of the functional equation; algorithm for computing the Selmer groups; 2-isogenies; generators of the Mordell-Weil groups
UR - http://eudml.org/doc/206945
ER -

References

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  2. [B-S] B. J. Birch and H. P. F. Swinnerton-Dyer, Elliptic curves and modular functions, in: Modular Functions of One Variable IV, Antwerpen 1972, Lecture Notes in Math. 476, Springer, 1975, 2-32. Zbl1214.11081
  3. [Fo] H. G. Folz, Ein Beschränktheitssatz für die Torsion von 2-defizienten elliptischen Kurven über algebraischen Zahlkörpern, Dissertation, Universität des Saarlandes, 1985. 
  4. [H-M] T. Honda and I. Miyawaki, Zeta-functions of elliptic curves of 2-power conductor, J. Math. Soc. Japan 26 (1974), 362-373. Zbl0273.14007
  5. [Ko] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, New York, 1984. Zbl0553.10019
  6. [Og] A. Ogg, Abelian curves over 2-power conductor, to appear. 
  7. [Sc] S. Schmitt, Berechnung der Mordell-Weil Gruppe parametrisierter elliptischer Kurven, Diplomarbeit, Universität des Saarlandes, 1995. 
  8. [Si] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. Zbl0729.14026
  9. [Si-Ta] J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer, 1985. 
  10. [S-T] R. J. Stroeker and J. Top, On the equation Y² = (X+p)(X²+p²), Rocky Mountain J. Math. 27 (1994), 1135-1161. Zbl0810.11038
  11. [Ta] J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, in: Modular Functions of One Variable IV, Antwerpen 1972, Lecture Notes in Math. 476, Springer, 1975, 33-52. 
  12. [We] E. Weiss, Algebraic Number Theory, McGraw-Hill, 1963. 
  13. [Zi] H. G. Zimmer, A limit formula for the canonical height of an elliptic curve and its application to height computations, in: Number Theory, R. Mollin (ed.), Proc. First Conf. Canad. Number Theory Assoc., Banff, 1988, de Gruyter, 1990, 641-659. Zbl0738.14020

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